The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function

  title={The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function},
  author={Christian Berg and Antonio J. Dur'an},
  journal={Mathematica Scandinavica},
We study the fixed point for a non-linear transformation in the set of Hausdorffmoment sequences, defined by the formula: T ((an))n = 1/(a0+�E �E �E+an).We determine the corresponding measure�E, which has an increasing and convex density on ]0, 1[, and we study some analytic functions related to it. TheMellin transform F of �E extends to ameromorphic function in the whole complex plane. It can be characterized in analogy with the Gamma function as the unique log-convex function on ].1… 

Figures from this paper

On an Iteration Leading to a q-Analogue of the Digamma Function
We show that the q-Digamma function ψq for 0<q<1 appears in an iteration studied by Berg and Durán. This is connected with the determination of the probability measure νq on the unit interval with
On Markov Moment Problem and Related Results
New results and theorems on the vector-valued Markov moment problem are proved by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result.
From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications
The aim of this review paper is to recall known solutions for two Markov moment problems, which can be formulated as Hahn–Banach extension theorems, in order to emphasize their relationship with the
On Markov Moment Problem and Mazur-Orlicz Theorem
Applications of the generalization of Mazur-Orlicz theorem to concrete spaces are proved. Suitable moment problems are solved, as applications of extension theorems of linear operators with a convex
On truncated and full classical Markov moment problems
Abstract Giving necessary and sufficient conditions for the existence of solutions of truncated and full classical Markov moment problems in terms of the given (or measured) moments, in Lp,μ (S) (1 ≤
Moment problems and orthogonal polynomials
In 1894 Thomas Jan Stieltjes (1856-1894) published an extremely influential paper: Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse, 8, 1–122; 9, 5–47. He introduced what is now known
Moment Problems on Bounded and Unbounded Domains
Using approximation results, we characterize the existence of the solution for a two-dimensional moment problem in the first quadrant, in terms of quadratic forms, similar to the one-dimensional
On the Moment Problem and Related Problems
Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence (yj)j∈ℕn  of real numbers and a closed
Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications
This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under
Markov Moment Problem in Concrete Spaces Revisited
This review paper starts by recalling two main results on abstract Markov moment problem. Corresponding applications to problems involving concrete spaces of functions and self-adjoint operators are


A transformation from Hausdorff to Stieltjes moment sequences
We introduce a non-linear injective transformation τ from the set of non-vanishing normalized Hausdorff moment sequences to the set of normalized Stieltjes moment sequences by the formulaT[(an)n=1∞]n
The Markov moment problem and de Finetti’s theorem: Part I
Abstract.The Markov moment problem is to characterize sequences admitting the representation sn=∫01xnf(x)dx, where f(x) is a probability density on [0,1] and 0≤f(x)≤c for almost all x. There are
Some Transformations of Hausdorff Moment Sequences and Harmonic Numbers
Abstract We introduce some non-linear transformations from the set of Hausdorff moment sequences into itself; among them is the one defined by the formula: $T\left( {{\left( {{a}_{n}} \right)}_{n}}
On Powers of Stieltjes Moment Sequences, I
For a Bernstein function f the sequence sn=f(1)·...· f(n) is a Stieltjes moment sequence with the property that all powers snc,c>0 are again Stieltjes moment sequences. We prove that $$s_n^c$$ is
Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
1 Introduction to Locally Convex Topological Vector Spaces and Dual Pairs.- 1. Locally Convex Vector Spaces.- 2. Hahn-Banach Theorems.- 3. Dual Pairs.- Notes and Remarks.- 2 Radon Measures and
Monotone Matrix Functions and Analytic Continuation
I. Preliminaries.- II. Pick Functions.- III. Pick Matrices and Loewner Determinants.- IV. Fatou Theorems.- V. The Spectral Theorem.- VI. One-Dimensional Perturbations.- VII. Monotone Matrix
Sur les cônes convexes de Riesz et les noyaux de convolution complètement sous-harmoniques
Soit X un groupe abélien localement compact et dénombrable à l’infini; ζ sera sa mesure de Haar. Dans les articles précédents [10] et [11], pour un noyau de convolution de Hunt N sur X, nous avons
Infinite Divisibility of Probability Distributions on the Real Line
infinitely divisible distributions on the nonnegative integers infinitely divisible distributions on the nonnegative reals infinitely divisible distributions on the real line self-decomposability and
Ueber die Grenzwerthe der Quotienten
DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen,
The Classical Moment Problem.